Goofs

Factual errors

It is highly unlikely that a submarine traveling on the surface, and acting as an icebreaker at the same time, would be able to keep up with vehicles traveling on the surface of the ice. Granted, the vehicles probably can't get up to full speed with the traction issues involved in driving on ice, but the NATO-designated Akula class submarine (Russian designation "Shchuka-b" class) only has a top speed of approximately 12mph while surfaced. Add in the fact it's breaking through ice at the same time, Hobbs and the gang would have made it to the sea locks with plenty of time to spare.

After Dom is captured/lured to the side of Cipher, there's basically no time Dom can make arrangement for him to meet up with Shaw's mother, as well as having the two ex crew to cover up his meeting with Shaw's mother and knowing all the blind spot in the meet up alley.

In making his escape in the sub factory Vin Diesel's car smashes into and pushes an armored vehicle out of the way, smashing it into a building but his car emerges out of the dust and flames without a mark on the front.

Errors in geography

Most of the streets seen in parts set in Manhattan are bidirectional, based on the road markings visible throughout. Nearly every major thoroughfare in Manhattan runs in one direction, however, making it obvious that the scenes were not filmed on location.

One establishing scene, shown in both the film and one of its trailers, shows the team driving northbound on Broadway past Times Square before their confrontation with Dom. In reality, Broadway is a one-way southbound street, and furthermore, most of its blocks in the Times Square vicinity are closed off to vehicular traffic.

Several Manhattan scenes, including the one where Dom stops to "fix" his car, take place in alleyways. In reality, Manhattan has only a handful of alleys, none of them in the vicinity of Midtown where Dom stopped.

Poltava is in Ukraine, not in Russia as Roman Pearce (Tyrese Gibson) mentions in the movie. Yalta is in former Ukrainian territory of Crimea which was annexed by the Russian Federation on 18 March 2014. As of 2017, the United Nations still maps Crimea as belonging to Ukraine.

Factual errors

The heat-seeking missile launched at Dom would've hit Dom in a matter of seconds. The slowest heat-seeking missile, has a speed of Mach 2.5 which is a bit faster than a bullet. There is no way a car running on ice at approx 80 mph would've outrun a missile coming at him at 1,900 mph.

There is no way the Akula Class submarine could have come remotely close to keeping up with the vehicles on the surface, let alone overtaking them. Even though the Akula was rated as one of the fastest submarines in the world during the cold war, with a reported top speed of between 28-35 knots (32-40 mph) this would be far from what the cars and trucks were apparently doing speed-wise even IF the reported top speed was DOUBLE what has been reported at 70 knots (80 mph). The part where the submarine broaches (comes to the surface) and overtakes the vehicles WHILE cutting through the ice is comical as the Akula classes reported surface speed is 10-12 knots (11-13 mph). A knot is only a measurement of a nautical mile per hour which is equivalent to about 1.15 mph.

Dom drives against, and beats his competitor in reverse. Reverse gear Is similar ratio to that of a forward first gear. It would be impossible to drive a basic car in reverse and beat someone who is at max speed in a forward gear.

When Dom is cutting a hole in the gas tank of the Russian Limo with the saw, the sparks from doing that would have ignited the gas fumes and the resulting fire would have negated the threat of the flare.

Dom uses a coke tab to remove a vacuum line off the engine. Letty ask if the car can handle that much boost. In fact, if you remove a vacuum line off a turboed engine, you will get less boost, and less power. It also appears it is getting removed from the distributor which will lessen the timing, removing more power from the engine.

Although the Akula class submarine depicted in the movie does, in fact, fire surface to air missiles in real life the launcher is located in the submarine's sail not hull and the missiles are Igla missiles which are in sealed tubes, not mounted on a rail.

The heat seeking missile which Dom tricks into hitting the submarine, causes a secondary explosion. The only way that is possible is if it causes the torpedoes to explode which are not located in the sail (location of the missile strike) and the missile's explosive is not strong enough to breach the hull to set off a torpedo. Dom didn't need his team's protection.
Additionally, it was a miracle how they all came to a stop from high speed on the ice in order to protect him from that secondary explosion.
Last, the explosion would not have stopped the submarine in its tracks as the engine room in the rear of the ship would have kept pushing the ship along with the inertia of the ship itself, if you believe it could drive through the ice in the first place.

Torpedo shown in movie is the incorrect size. Actual torpedo used in this type of ships are type 53 and type 65. Smaller ones (type 53) ar more than 7 meters long (that is length almost 2 cars) and weights more that 2 tons. What is way more than any human car raise with one hand. The one shown in movie is maybe 2 or 3 meters long, and weights maximum 150-200 kilos (considering almost inhuman strength of Hobbs).

In the chase scene set in Berlin, the team is chased by the police. The police vehicles use a very narrow kind of LED flashlight mounted on the roof. However, this kind is not used on police vehicles operating in Germany.

The NYPD vehicles used in Manhatten in the chase scene used all blue lights. In reality, NYPD follow NY state emergency lighting code (NYVTL § 375 (41)), which allows police to only use Red and white for forward facing lights, where blue may be expressed only to the rear of the vehicle. NYPD also do not use those types of light bars.

Miscellaneous

when Vin jumps outside of his car at the end of the first race, the curb of the sidewalk and the hole of the sewer are very huge, as much as Vin! (VFX fault)
The sky in this and the next shot are VFX composition and are too blue and dark, isn't believable...at the next shot, with the car jumping, has real sky, with more exposition.

Plot holes

Even in the realm of these movies, it is quite inconceivable that the Russian military would not be able to change the codes for the atomic rockets in the time the team needs to travel from the United States to Russia.

The tracking device in Dom's cross has a red blinking light. If the aim is to provide tracking without being detected, a red blinking light is the last thing you'd want. This is a common error in movies with trackers placed on cars and such. It shows the audience the device is active, but it makes no sense whatsoever.

Even if an aircraft could be able to find radar blind spots to fly undetected, it needs to land for refueling. A plane as large as Cipher's (which appears to be a modified Boeing 787) needs large, conventional, commercial airports for such a need.

When Dom says to the team to "head to the shore", they can hear him. But how? The team has communication equipment in their cars to talk to each other, but his car wasn't outfitted by them. He would have had to figure out their frequency and possibly encryption to be able to talk to them.

At the end of Fast and The Furious 6, when they find Letty, Brian and Mia's son Jack is an infant. This is when Dom and Elena broke up. In Furious 7, Jack is school aged. When this movie starts Elena's son is an infant, which means that Elena's son is too young to be Dom's child.

In a scene where the crew is being chased on the ice, the camera slows down to show bullet casings flying by the camera for cinematic effect. You can clearly see the crimped edges of the casings, revealing they are blank cartridges.

Spoilers

The goof item below may give away important plot points.

Factual errors

Cipher's plan involves launching a nuclear missile from a captured Russian submarine. However, the submarine shown, and as stated by Tej's tablet, is an Akula-class submarine (the NATO designation). The Akula is an attack submarine, and as such does not carry nuclear missiles, which are carried by "boomers."

However, the Typhoon-class "boomer" submarine, as seen in The Hunt for Red October (1990), does carry nuclear missiles, and its Russian designation is Akula.